登录

An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on the values. For addition and subtraction, propagating the uncertainty requires us to express the absolute uncertainty of the outcome, which is the square root of the sum of absolute uncertainties for all steps. For multiplication and division, propagating uncertainty requires us to find the square root of the sum of the relative uncertainties for all steps, and this square root is equal to the relative uncertainty of the outcome, also known as the ratio between the absolute uncertainty of the outcome and the magnitude of the expected outcome. For exponential functions, we propagate the uncertainty by multiplying the power with the relative uncertainty of the base value, which then equates to the relative uncertainty of the outcome for the whole data set. Knowing how to propagate uncertainty correctly helps us identify the method that yields the least uncertainty, therefore optimizing our experimental protocols.

Tags
Propagation Of UncertaintyRandom ErrorStatistical AnalysisAbsolute UncertaintyRelative UncertaintyArithmetic OperationsAdditionSubtractionMultiplicationDivisionExponential FunctionsExperimental ProtocolsUncertainty Optimization

来自章节 1:

article

Now Playing

1.10 : Propagation of Uncertainty from Random Error

Chemical Applications of Statistical Analyses

410 Views

article

1.1 : SI Units: 2019 Redefinition

Chemical Applications of Statistical Analyses

1.1K Views

article

1.2 : Degrees of Freedom

Chemical Applications of Statistical Analyses

2.8K Views

article

1.3 : Statistical Analysis: Overview

Chemical Applications of Statistical Analyses

3.9K Views

article

1.4 : Types of Errors: Detection and Minimization

Chemical Applications of Statistical Analyses

1.1K Views

article

1.5 : Systematic Error: Methodological and Sampling Errors

Chemical Applications of Statistical Analyses

1.1K Views

article

1.6 : Random Error

Chemical Applications of Statistical Analyses

597 Views

article

1.7 : Standard Deviation of Calculated Results

Chemical Applications of Statistical Analyses

3.6K Views

article

1.8 : Introduction to z Scores

Chemical Applications of Statistical Analyses

274 Views

article

1.9 : Uncertainty: Overview

Chemical Applications of Statistical Analyses

305 Views

article

1.11 : Propagation of Uncertainty from Systematic Error

Chemical Applications of Statistical Analyses

262 Views

article

1.12 : Uncertainty: Confidence Intervals

Chemical Applications of Statistical Analyses

2.8K Views

article

1.13 : Significance Testing: Overview

Chemical Applications of Statistical Analyses

3.2K Views

article

1.14 : Identifying Statistically Significant Differences: The F-Test

Chemical Applications of Statistical Analyses

1.2K Views

article

1.15 : Comparing Experimental Results: Student's t-Test

Chemical Applications of Statistical Analyses

1.3K Views

See More

JoVE Logo

政策

使用条款

隐私

科研

教育

关于 JoVE

版权所属 © 2025 MyJoVE 公司版权所有,本公司不涉及任何医疗业务和医疗服务。